The minimax theorem states that every two-person finite game that is a zero-sum game has optimal mixed strategies. It was proved by John von Neumann in 1928.
Formally, let 
and 
be mixed strategies for players A and B. Let 
be the payoff
matrix. Then
 |
where 
is called the game value and 
and 
are optimal mixed strategies.
It also turns out that if there is more than one optimal mixed
strategy, there are infinitely many.
In the Season 4 opening episode "Trust Metric" (2007) of the television crime drama NUMB3RS, math genius Charlie Eppes mentions that he used the minimax theorem in an attempt to derive an equation describing friendship.
